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81.

The probability distribution of a random variable X is given below

X = x | 0 | 1 | 2 | 3 |

P(X) = x | $\frac{1}{10}$ | $\frac{2}{10}$ | $\frac{3}{10}$ | $\frac{4}{10}$ |

Then the variance of X is

1

2

3

4

82.

The probability that an individual suffers a bad reaction from an injection is 0.001. The probability that out of 2000 individuals exactly three will suffer bad reaction is

$\frac{1}{{\mathrm{e}}^{2}}$

$\frac{2}{3{\mathrm{e}}^{2}}$

$\frac{8}{3{\mathrm{e}}^{2}}$

$\frac{4}{3{\mathrm{e}}^{2}}$

84.

A committee of 12 members is to be formed from 9 women and 8 men. The number of committees in which the women are in majority is

2720

2702

2270

2278

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85.

In an entrance test there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student know the answer to a question is 9/10. If he gets the correct answer to a question, then the probability that he was guessing is

$\frac{37}{40}$

$\frac{1}{37}$

$\frac{36}{37}$

$\frac{1}{9}$

86.

There are four machines and it is known that exactly two of them are faulty. They are teste done by one, in a random order till both the faulty machines are identified. Then, the probability that only two tests are need is

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{1}{2}$

$\frac{1}{4}$

87.

A random variable X has the probability distribution given below.

X | 1 | 2 | 3 | 4 | 5 |

P(X = x) | K | 2K | 3K | 2K | K |

Its variance is

$\frac{16}{3}$

$\frac{4}{3}$

$\frac{5}{3}$

$\frac{10}{3}$

88.

A six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be 7. The probability that the number 3 has appeared atleast once, is

$\frac{1}{5}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

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89.

If A, B and C are mutually exclusive and exhaustive events of a random experiment such that P(B) = $\frac{3}{2}$P(A) and P(C) = $\frac{1}{2}$P(B), then P(A ∪ C) equals to

$\frac{10}{13}$

$\frac{3}{13}$

$\frac{6}{13}$

$\frac{7}{13}$

90.

The letters of the word 'QUESTION' are arranged in a row at random. The probability that there are exactly two letters between Q and S is

$\frac{1}{14}$

$\frac{5}{7}$

$\frac{1}{7}$

$\frac{5}{28}$

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